The present invention relatees generally to a novel optical system, and particularly to an optical system which provides light of excellent uniformity of intensity, without any illuminance reduction in the peripheral area of an object, so that it is particularly useful for an exposure system applicable to exposure of printed circuit boards, integrated circuits or the like, for an exposure system applicable to contact exposure apparatus for plate making, step-and-repeat machines or the like, and for an illumination system applicable to copy machines or the like.
It is well known that such a conventional condenser optical system as shown in FIG. 27 has been used in an illumination system which is intended to provide an illumination light for an entire object area uniformly and effectively. The conventional condenser optical system, referring to FIG. 27, comprises a condenser lens C and a field lens F. The condenser optical system is designed so that the real image of a light source LS, which is placed in front of the condenser lens C, is formed adjacent to the field lens F, and that the real image of an entrance pupil A of the condenser lens C is formed on an object S which is placed behind the field lens F.
The conventional condenser optical system, however, raises a serious problem, i.e. the illuminance in the peripheral area of the object is reduced, as shown in FIG. 28, in accordance with the cosine fourth law. For instance, referring to FIG. 27, the illuminance at the point on the object, where the exit angle .theta. forms 27 degrees relative to the optical system, is less than that at the point on the optical axis, i.e. the point where the exit angle .theta. forms zero degrees.
There are several reasons, other than the above-mentioned cosine fourth law, for the occurrence of illuminance reduction in the peripheral area of the object, which will be discussed in detail later. Actually, the illuminance in the peripheral area of the object is reduced less than a value derived from the cosine fourth law. According to the simulation calculation made by applying lens data listed in Table 1 to the optical system shown in FIG. 27, it is found that the illuminance at the point where the exit angle .theta. forms 27 degrees, is reduced by about 50 percent in comparison with the illuminance at the center thereof.
TABLE 1 ______________________________________ r d n ______________________________________ 1 0.77 0.37 1.5 2 .infin. 0.46 3 0.77 0.37 1.5 4 .infin. ______________________________________ f = 1, distance from the light source = 50, distance from the object = 100
FIG. 29 shows an illuminance distribution on the object S, which is obtained by using the optical system shown in FIG. 27, in the case where a point source is positioned on the optical axis at the distance of 50 from the optical system. FIG. 30 shows an illuminance distribution of the meridional ray on the object S, and FIG. 31 shows an illuminance distribution of the sagittal ray on the object S, in each of which the point source is positioned away by 14 from the optical axis and at a distance of 50 from the optical system. The respective vertical axis of FIGS. 29 through 31 depicts a relative illuminance, in which the illuminance of the center of the object S is regarded as 100 percent when the point source is positioned on the optical axis. On the other hand, the respective horizontal axis of FIGS. 29 through 31 depicts a position on the object S. In FIGS. 29 through 31, the position denoted by 50 in radius corresponds to the position on which the exit light from the optical system is impinged.
As mentioned above, the illuminance in the peripheral area of the object S is actually reduced less than a value derived from cosine fourth law. One of the reasons therefor is an aberration, because the cosine fourth law is on the premise that an optical system has no aberration, whereas an actual optical system inevitably has the aberration.
Accordingly, it has conventionally been practiced that an optical system is designed so that the aberration be eliminated as far as possible, in other words it has commonly been practiced that an optical system is designed so as to satisfy the sine condition. Thus, even in an illumination system design, the optical system for use in illumination has conventionally been designed so as to satisfy the sine condition, because it has been believed as a matter of course by a person skilled in the art.
It has been found by the inventor, however, that designing an optical system so as to satisfy the sine condition causes an illuminance reduction in the peripheral area of the object to be illuminated.
Now, discussion is given with regard to the reasons why the illuminance reduction in the peripheral area of the object will be caused.
Referring to FIG. 32, which is a schematic view of a typical optical system shown in FIG. 27, light emitted from the light source LS enters into the optical system at the entrance height h, in this case the light source LS can be regarded as being placed at an infinite distance from the optical system, because it is positioned at a far distance from the optical system in comparison with the focal length thereof. The real image of the light source LS is formed at a point P, and the light goes through an exit pupil at an exit angle .theta.. Satisfying the sine condition means that the sine of the exit angle .theta. is proportioned to the entrance height h, accordingly the relation can be expressed by the following formula (1): EQU h=k.sub.1 sin .theta. (1)
where k.sub.1 is a proportional constant.
The light which entered into the optical system at the entrance height h exits therefrom to impinge on the point Q of the object S. Then, sin .theta. can be expressed by the following formula (2): ##EQU1## where H is the distance between the point Q and the center of the object S (hereinafter referred as illumination height), and a is the distance between the point P and the point Q.
Accordingly, it can be transformed from the formulae (1) and (2), as follows: ##EQU2##
As can be understood from FIG. 32, when the entrance height h is increased, the exit angle .theta. will become large, hence the illumination height H will be increased in accordance therewith, and similarly the distance a between the point P and the point Q will also be increased. In the case that the entrance height h is increased at a constant rate, the illumination height H will be rapidly increased more than the increase of the entrance height h, since the illumination height H is proportioned to the product of the distance a and the entrance height h, as can be seen from the formula (3). Accordingly, the relationship between the incident light radius A.sub.o around the optical axis of the entrance pupil A and the radius S.sub.o of the illumination area of the object S, similarly to the relationship between the entrance height h and the illumination height H, is that the radius S.sub.o increases at a greater rate than the rate that the radius A.sub.o increases, from which it will be apparent that the illuminance on the object S will be reduced as it goes away from the optical axis, in comparison with that on the entrance pupil A.
Indeed in an image-formation optical system design it will be necessary to design the optical system so as to satisfy the sine condition because it is important to minimize the aberration, but in an illumination optical system design there is no need to do so. Furthermore, designing to satisfy the sine condition causes the illuminance reduction in the peripheral area of the object to be illuminated, as mentioned above.
In a conventional illumination system, it has been practiced in order to correct the illuminance reduction in the peripheral area of the object, that a gradient filter is placed in the optical path thereof, or that the light source is placed at a sufficient distance from the object. These conventional correction methods are, however, disadvantageous in view of the fact that light quantity is considerably reduced in the entire area of the object in the former method, and that the illumination system inevitably becomes large in size in the latter.